“I believe Geneva airport serves both France and Switzerland.”: this is correct. But contrarily to Basel airport, GVA is in Switzerland (with an exit to France that has nothing to envy to the late Berlin wall).
“airlines registered in Switzerland honour EU passenger rights when the flight arrives into the EU”: while this is what the linked page is telling, I still think it is wrong. To my knowledge, are bound to EU261:
– Airlines based in the EU
– Other airlines for flight leaving the EU
Check Article 3.1 of the regulation (there: http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2004:046:0001:0007:EN:PDF)